Question

x.�i5ss="problemIntroduction" id="imagePI">A uniform ladder with
mass and length rests against a smooth wall. A do-it-yourself enthusiast of mass
stands on the ladder a distance from the bottom (measured along the ladder). The ladder
makes an angle with the ground. There is no friction between the wall
and the ladder, but there is a frictional force of magnitude
between the floor and the ladder. is the magnitude of the normal force exerted by
the wall on the ladder, and is the magnitude of the normal force exerted by the
ground on the ladder. Throughout the problem, consider
counterclockwise torques to be positive. None of your answers
should involve (i.e., simplify your trig functions).

Part A

What is the minimum coeffecient of static
friction required between the ladder and the ground so that the
ladder does not slip?

Express in terms of , , , , and .

=

Part B

Suppose that the actual coefficent of
friction is one and a half times as large as the value of
. That is, . Under these circumstances, what is the magnitude
of the force of friction
Express your answer in terms of , , , , , and . Remember to pay attention to the relation of force and
.